Answer:
The relation between x and y is
![y=\frac13 x^2](https://tex.z-dn.net/?f=y%3D%5Cfrac13%20x%5E2)
Step-by-step explanation:
Given that,
The value of y varies directly as the square of x.
![y\propto x^2](https://tex.z-dn.net/?f=y%5Cpropto%20x%5E2)
![\Rightarrow y=rx^2](https://tex.z-dn.net/?f=%5CRightarrow%20y%3Drx%5E2)
where r is constant of proportional.
Given that,
y= 27 and x=9
Plug y= 27 and x=9 in above relation
![y=rx^2](https://tex.z-dn.net/?f=y%3Drx%5E2)
![\therefore 27=r(9)^2](https://tex.z-dn.net/?f=%5Ctherefore%2027%3Dr%289%29%5E2)
![\Rightarrow 27 = r.81](https://tex.z-dn.net/?f=%5CRightarrow%2027%20%3D%20r.81)
![\Rightarrow r=\frac{27}{81}](https://tex.z-dn.net/?f=%5CRightarrow%20r%3D%5Cfrac%7B27%7D%7B81%7D)
![\Rightarrow r=\frac{1}{3}](https://tex.z-dn.net/?f=%5CRightarrow%20r%3D%5Cfrac%7B1%7D%7B3%7D)
The relation between x and y is
![y=\frac13 x^2](https://tex.z-dn.net/?f=y%3D%5Cfrac13%20x%5E2)
Since
represents the number of years passed since 2005, in 2005 we have
, and in 2015 we have
. Let
represent the profits of Jones and Davis, respectively, at year y.
We have
![P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9](https://tex.z-dn.net/?f=P_J%282005%29%20%3D%2010%280.99%29%5E0%20%3D%2010%2C%5Cquad%20P_J%282015%29%20%3D%2010%280.99%29%5E%7B10%7D%5Capprox%209)
![P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9](https://tex.z-dn.net/?f=P_D%282005%29%20%3D%208%281.01%29%5E0%20%3D%208%2C%5Cquad%20P_D%282015%29%20%3D%208%281.01%29%5E%7B10%7D%5Capprox%209)
Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor
goes to zero as t grows.
On the other hand, Davis starts with a smaller value, but
tends to infinity as t grows.
So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.
More precisely, we have
![8\cdot 1.01^t = 10\cdot 0.99^t \iff 0.8 = \left(\dfrac{0.99}{1.01}\right)^t \iff t\approx 11](https://tex.z-dn.net/?f=%208%5Ccdot%201.01%5Et%20%3D%2010%5Ccdot%200.99%5Et%20%5Ciff%200.8%20%3D%20%5Cleft%28%5Cdfrac%7B0.99%7D%7B1.01%7D%5Cright%29%5Et%20%5Ciff%20t%5Capprox%2011%20)
So, after 11 years, Davis will overcome Jones.
Divide the number of guest that came by the number of guests invited: 104/125=.832 or 83%. 83% of the invited guests were there :)
Answer:
T(a) =(a+2)/11
Step-by-step explanation:
The inverse of the inverse is the function
To find the inverse let T^-1(a) be y
y = 11a -2
Exchange y and a
a = 11y -2
Solve for y
Add 2 to each side
a+2 = 11y -2 +2
a+2 =11y
Divide each side by 11
(a+2)/11 =y
T(a) =(a+2)/11
Answer:
4
Step-by-step explanation: